let x be an infinite set and let ta be a topology on x in which all infinite subsets of x are open show that ta is the discrete topology.

Q: Which of the following equations does not represent an ellipse? * x² + 2y² - 16 = 0 Option 1 x² +…

A:

Q: 5. Let a₁ = √5, (a) Find the recursion formula (b) Assuming the sequence converges find its limit…

A:

Q: 4. Using Laplace transform methods, solve for t≥ 0 the following simultaneous differential equation…

A:

Q: Write the statement in symbolic form: "BBM and Sara Duterte may have won the election but Leni and…

A:

Q: The Minimum point of y = 8x+4 (x-2)²

A: Use a graphing utility to plot the function. Use the utility to determine the minimum point.

Q: 16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from school each…

A: since you have asked a question with multiple sub parts, we will solve the first three subparts for…

Q: Use A-1 to decode the cryptogram.

A: Given,         A=122379-4-114

Q: Determine the values of a where the function f (x) is not continuous. Label each discontinuity as…

A: Given function is continous for all real values of x.  As per given instructions,  Enter NA in both…

Q: The number of bacteria in a container is given by an equation, Q(t)= Qoekt, where t is measured in…

A:

Q: a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of…

A: "As per the policy we are allowed to answer only 3 subparts at a time, I am providing the same.…

Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

A:

Q: 1. Find the Laplace transform of the following function using the basic -5t definition and…

A:

Q: 1. Evaluate the solution for the following differential equation y" - 2y + y = 2. Find the general…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: e 1. If F(x) = [ dt, find F(1) and F'(x).

A:

Q: Find f '(x) and f "(x) at x = 0 using finite difference approximation of O(h²). (Hint: you have to…

A: The table given is as follows: x 0 0.1 0.2 0.3 0.4 fx 1 0.9048 0.8187 0.7408 0.6073 We are…

Q: (a) Use the method of Lagrange multipliers to determine the minimum and maxi values of f(x, y) = x²…

A:

Q: The relationship between training costs (x) and productivity () is given by the following formula, y…

A: Given- The relationship between training costs (x) and productivity (y) is given by the following…

Q: 3. Consider the double-integral 2xy² + 2 dx dy where D is the triangle with vertices (0,0), (5, 1)…

A:

Q: The number of people in a small country town increases by 2% per year. If the population at the…

A: Solution :   Given that The principal population P0 = 12500 Increasing rate r = 2% = 2/100 = 0.02  n…

Q: 2. Evaluate: v2-du

A: A definite integral of a real valued function fx is the area under the curve y=fx between the two…

Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

A: Solution : Let A be quantity of radium present at time t. Decomposition equation, dAdt∝A dAdt=-kA…

Q: 4-x²-y² 1 Evaluate ²4-y² So coordinates. x²+y²+z² dzdxdy by using spherical or cylindrical

A: Here we can use spherical coordinates to find the value of the integral. In spherical coordinates…

Q: Consider these functions: f(x) = 3 and g(x) = 3+2-5

A: Given,          f(x)=3x,   and     g(x)=3x+2-5

Q: Numerical Integration: 2 1 ² 1. =dx Jo √x

A: As per the question we are given a definite integral and we have to solve it numerically. Here we…

Q: 4. Given z = x-y x+y Find əz/ax

A:

Q: Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following…

A:

Q: 1. Given the set A = {1,2,3,4,5,6}. Given S6 = {f: A→ Alf bijective mapping} is a group with respect…

A:

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. In(x+1)³ 3. Lim 3 X→∞0 6x

A: Solution

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2. Lim: xcosx X-0 sin ²x 2

A: The output of the function changes with the input. If the function f(x) has the limit L at x=a, then…

Q: 4. A 5-nC point charge is located at (-2,1,3) in free space. Find (a) E at the origin (b) E at point…

A:

Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

A:

Q: 41. Find the interquartile range from this box-and-whisker plot. 10 31 68 80 A. 31 B. 21 C. 58 D. 80

A: We know , Interquartile range = Q3 - Q1

Q: Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y2 + 144y + 11yy' -…

A: Solution: Given I=∫01-16y2+144y+11yy'-4y'2dx and y(0)=8 and y(1)=8.6 Now, By Euler Lagrange Equation…

Q: use Newton’s Method to find the root of the given equation, accurate to six decimal places, that…

A: The equation in the form f(x)=0 is called a transcendental equation. The solution of the equation is…

Q: The Laplace transform of the function u: [0, ∞) → R [(t-2)² + (t-2) sin(5(t-2)), for t > 2, =…

A:

Q: Let d(x, y) = be a metric on R* then the open ball of center 2 and radius is: O ]1/2,1[ O None of…

A: I have used definition of open ball in metric space.

Q: 5. Neil is traveling on a road at 60 miles per hour when he slams his foot on the brake pedal in…

A: S=(30Dfn) Here, S is speed of vehicle in miles/hour. 30 is constant.  D is skid distance in feet. f…

Q: Find the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² 4 and the…

A:

Q: 63. Multiple Choice Let A be the region bounded by the graphs of y = 4√x, y = 4, and x = 0. What is…

A:

Q: theormo- Let (Fot..) is a field and f(x) EF(x) then the ideal is maximals ideal iff fex) is an…

A: Let F be a field. Here , f(x) ∈ Fx. Here , First we assume that , f(x) is maximal ideal in Fx. We…

Q: Use multiple equation Newton-Raphson method to determine one of the roots of the following…

A: Given x2+3y2=10x-22+y-12=3

Q: The hyperbola with the given equation is centered at? * 16y² -9x² +36x + 96y - 36 = 0

A:

Q: Let K denote the algebraic closure of Fp P

A:

Q: Q4: A vertical steel plate of dimensions 3cm x 3cmamd negligible thickness is in steady state…

A:

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: To evaluate the definite integral ∫abfxdx, use the following midpoint rule formula.…

Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

A: As per norms, we will be answering only the first question. If you need an answer to others, then…

Q: 3. Solve the following differential equations using Laplace transforms: d³x d²x dx + + dx d²x b. +x=…

A:

Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: Introduction: A rate of chage is the ratio of two related quantities in different units in…

Q: (3 min) Is the proposition (pvq)^(pv¬q)^(pv¬q)^(pv q) satisfiable? True False

A: First we construct the truth table for the given proposition. We use "T" for "True" and "F" for…

Q: X L479 1 4 11 f(x) 12 -23 -15 33 -13

A: Lagrange's interpolation polynomial for n points can be defined as:…